Immunotherapy and Nodal-Sparing Irradiation for T-Cell Induction and Unmasking of Tumor Antigenicity in the Microenvironment for Head and Neck Cancer

Inclusion Criteria: * Patients 18 years or older. * Patients with surgically resectable squamous cell carcinoma of the oral cavity or HPV-negative squamous cell carcinoma of the oropharynx. Resectability will be determined by the treating surgeon. Patients must have locoregionally advanced disease defined by clinical T3-4 staging and/or clinical node positive staging. * A CPS score of at least 1 on initial biopsy. * Zubrod, or Eastern Cooperative Oncology Group (ECOG) performance status 0-2. * Pregnancy. It is not known what effects this treatment has on human pregnancy or development of the embryo or fetus. Therefore, female patients participating in this study should avoid becoming pregnant, and male patients should avoid impregnating a female partner. Non-sterilized female patients of reproductive age and male patients should use effective methods of contraception through defined periods during and after study treatment as specified below. Female patients must meet one of the following: * Postmenopausal for at least one year before the screening visit, OR * Surgically sterile (i.e., undergone a hysterectomy or bilateral oophorectomy), OR * If subject is of childbearing potential (defined as not satisfying either of the above two criteria): * Agree to practice two effective methods of contraception (combination methods requires use of two of the following: diaphragm with spermicide, cervical cap with spermicide, contraceptive sponge, male or female condom, hormonal contraceptive, intrauterine device, etonogestrel implant, etc.) from the time of signing of the informed consent form through 90 days after the last dose of study agent, AND * Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptom-thermal, post ovulation methods\] and withdrawal are not acceptable contraception methods). Male patients, even if surgically sterilized (i.e., status post vasectomy), must agree to one of the following: * Practice effective barrier contraception during the entire study treatment period and through 90 days after the last study drug dose, OR * Must also adhere to the guidelines of any study-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptom-thermal, post ovulation methods\] and withdrawal are not acceptable methods of contraception.) - Ability to understand a written informed consent document, and the willingness to sign it. Exclusion Criteria: * HPV-positive squamous cell carcinoma of the oropharynx. * Tumor inaccessible for clinic-based biopsy as determined by the treating surgeon. * Solid organ transplant requiring chronic immunosuppression. * Autoimmune disease requiring use of steroids or chronic immunosuppression. * Prior invasive malignancy within the past 3 years (except for T1a surgically treated melanoma with negative margins, any early-stage non-melanomatous skin cancer, early-stage prostate cancer, or differentiated thyroid cancer). Patients with benign non-metastasizing tumors are eligible. * Life expectancy less than 12 months. * Performance status Zubrod ≥ 3. * Patients with prior external beam radiation therapy (RT) to the head and neck that overlaps the expected treatment fields. a. Note: Patients receiving prior Iodine-131 therapy will be eligible. * Prior systemic therapy, including cytotoxic chemotherapy, biologic/targeted therapy, or immune therapy for the study cancer. * Body weight ≤ 30 kg. * Any of the following severe laboratory abnormalities within 30 days of registration, unless corrected prior to it: 1. Sodium \< 125 mmol/L or \> 155 mmol/L 2. Potassium \< 3.5 mmol/L or \> 6 mmol/L 3. Glucose \> 400 mg/dl 4. Serum calcium (ionized or adjusted for albumin) \< 7 mg/dl or \> 12.5 mg/dl 5. Magnesium \< 0.9 mg/dl or \> 3 mg/dl * Unstable angina and/or congestive heart failure requiring hospitalization within three months of registration. * Transmural myocardial infarction within three months of registration. * Medical or psychiatric illness that would compromise the patient's ability to tolerate treatment or limit compliance with study requirements. * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception during treatment and for 6 months after radiation. This exclusion is necessary because the treatment involved in this study may be significantly teratogenic. Women who are breastfeeding are also excluded.