The goal of this clinical trial is to learn if drug CADI-05, when used together with pembrolizumab (an FDA approved immunotherapy), can help treat locally advanced head and neck squamous cell carcinoma (LA-HNSCC) in adults. It will also learn about the safety of drug CADI-05. The main questions it aims to answer are: * Does using CADI-05 together with pembrolizumab help the immune system fight cancer better and lead to better results for patients? * What side effects or health problems might happen when people receive these two treatments? Participants will: * Get pembrolizumab by IV (through a vein) once on day 1 of week 1 and again day 1 of week 4. This is standard of care treatment. * Get CADI-05 as a small injection into the skin once a week for 5 weeks. This is the experimental (research) treatment. * Visit the clinic every week for treatments, checkups and tests for 5 weeks. * Have surgery between week 6 and week 7. * Return to the clinic once for a follow-up visit about 30 days after surgery.
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Occurrence of dose limiting toxicities (DLTs) by CTCAE ver. 6.0. of CADI-05 and pembrolizumab in patients with surgically resectable LA-HNSCC during the toxicity assessment window.
Timeframe: From Day 1 of CADI-05 treatment until safety follow-up, for a total of up to 13 weeks.
Occurrence of Grade 3 and higher AEs by CTCAE ver. 6.0. of CADI-05 and pembrolizumab in patients with surgically resectable LA-HNSCC during the toxicity assessment period at the MTD of CADI-05.
Timeframe: From the first treatment of CADI-05 through study completion, an average of 27 months.