The lines at the terminal are policed by a contractor. I'm not sure if "Mint" counts as first class in their eyes. I've seen them let people through with First Class on US Airways and Virgin America, people with PreCheck, and current/retired military with ID.
Ironically, I was selected for random precheck (it actually wasn't very random, anyone in the regular line traveling alone was given a green PreCheck card) and got to go through security with everyone in the priority line. This was at 8 in the morning though, so your mileage may vary.