Additional Study Information: The purpose of the first part (Phase I) of the study is to test the safety of navitoclax in combination with dabrafenib and trametinibat different doses to find out what effects, if any, it has on people. There will be about 18 people treated in this part of the study. The purpose of the second part of this study (Phase II) is to compare the good and bad effects of navitoclax in combination with dabrafenib and trametinib to using the usual approach of dabrafenib and trametinib in patients with BRAF-mutant melanoma. This study will allow the researchers to know whether this different approach is better, the same, or worse than the usual approach. There will be 50 people taking part in this part of the study.