Since you don't know what sort of motor is controlling your drum motor, I would guess it's just a basic AC induction motor. That being said, the speed of the motor is based on the AC input frequency; 50/60 Hz. Due to the nature of conventional AC motors, this is not negotiable.

If you are willing to swap to a different electric motor, you could choose a multitude of DC options (Stepper, BLCD; which would require an AC/DC converter) or retrofit & learn the intricacies of the IMP AC motor (which still requires a swap).

Surely you are going to tell me that your appliance has a slow speed and faster speed built into the electronics already. If that's the case, look at the schematic that controls it (I've found schematics for every appliance I have had to work on that lives in my home on the internet). You may find clues there.

Bottom line, controlling speed with an AC motor involves WAY more than with a DC motor. If you could provide more information, those in the know may be able to zero you in on a more specific plan of action.