Radiation therapy uses high-energy x-rays to kill tumor cells. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. It is not yet known whether radiation therapy is more effective when given together with chemotherapy or alone after surgery in treating salivary gland tumors. This randomized phase II/III trial is studying radiation therapy with or without chemotherapy to see how well it works in treating patients with high-risk malignant salivary gland tumors that have been removed by surgery. Eligibility is being at least 18 years old and pathologically proven diagnosis of a malignant major salivary gland tumor or malignant minor salivary gland tumor of the head and neck. Contact Mercy clinical trials for further eligibility criteria.