A.H.
Alcohol is generally the best thing. If it is a gas dryer you want to be careful of solvents you use. Some could be explosive. Even with electric when it gets hot, solvents may smell up your other clothes.
I would see what I could get off with just regular rubbing alcohol- maybe get 91%. Good luck...
I thought I would add...
You might could try wax paper and a hot iron too...that works really well for candle wax- but basically gum is wax based too. I have always been told to use ice cubes and freeze gum but never had much luck... inexpensive to try though...