As mentioned, your in-dungeon level, and out-of-dungeon level are separated from each other. The reason most people skip mobs is because the xp you get at the end of the run is a fixed amount based on your character level. If you enter at lvl 53 outside, you get the same xp at the end no matter what you do inside the dungeon (usually a similar amount as the bonus xp from a leveling roulette).

Since you have to kill a certain amount of mobs inside the dungeon to unlock the exit, you'll end up with plenty of xp to raise your in-dungeon level just doing that. The only thing you should really be aiming for are the silver chests, and any gold/bronze chests that are unguarded, or that you would need to clear to get through the room anyway.