Motors provide torque, that's their primary job. The power rating (HP or kW) is just a shorthand notation of "so much torque at such and such a speed". The speed at which they provide it matters only in the application with regard to what is used to make it spin at the RIGHT speed for the task, while providing that designated torque.
AC induction motors produce their rated torque based upon the ratio of voltage and frequency applied to them, then industry design specs say +-10%. So a 380V 50Hz designed motor is based on 380/50 = 7.6 V/Hz, but because of EU harmonization programs for the various countries, they are usually designed to accommodate up to 415V 50Hz, so up to 8.3V/Hz.
If you provide it with 480V 60Hz, the V/Hz ratio is 480/60 = 8.0V/Hz. right in the bread basket for what that motor is going to expect. So do NOT go and buy that transformer! You will starve the motor for voltage; you end up with 380V 60Hz, and 380/60 = 6.33V/Hz, well under the 10% range of acceptability. The motor will produce about 50% of it's rated peak torque, slip will increase under the same load, the motor will pull more current and over heat (unless perchance it was designed at 120% of needed power capacity).
But as petersonra said, it's just not as simple as that either, because it depends on the load and the machine. We have no idea what kind of machine it is and whether or not it NEEDS to operate at the speeds associated with a 50Hz supply. But it MIGHT be a serious problem. If for example the load is a centrifugal pump, the added 20% speed will result in the pump demanding 173% motor power from that motor, so it will overload (unless you can adjust the flow in some other way). Also if it involves a cutting tool of some sort, many of those are highly engineered now so changing the speed can seriously damage the cutting surfaces.
Bottom line, I would ask the machine mfr if in any way possible.
