Dabrafenib and Trametinib Before and After Surgery in Treating Patients With Stage IIIB-C Melanoma With BRAF V600 Mutation

Inclusion Criteria: * Capable of giving written informed consent, which includes compliance with the requirements and restrictions listed in the consent form * Patients must have histologically or cytologically confirmed stage IIIB/C melanoma by American Joint Committee on Cancer (AJCC) version 7; the definition of resectability can be determined by the patient's surgical oncologist and verified via discussion at Multidisciplinary Tumor Conference attended by melanoma medical and surgical oncology staff; resectable tumors are defined as having no significant vascular, neural or bony involvement; only cases where a complete surgical resection with tumor-free margins can safely be achieved are defined as resectable * Multicenter sites: confirmation of diagnosis via histology or cytology will be made by the local site pathologist; likewise, resectability determination will be made by the site's multidisciplinary team * Patients must be medically fit enough to undergo surgery as determined by the surgical oncology team * BRAF mutation-positive melanoma (V600E or V600K) based on report from a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory * Patients must have measurable disease, defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Hemoglobin \>= 9.5 g/dL * Platelets \>= 100 x 10\^9/L * Prothrombin time/international no…