Alex,
The Allison T-56 on the C-130 is fairly unique among turboprop engines, in it's operation. Another common turboprop/turboshaft which operates in a similiar manner is the Garret TPE-331.
A turbofan or turbojet engine ("jet engine") does indeed vary RPM in order to effect a change in thrust. Thrust in a jet is non-linear. This means that at the bottom end of the RPM range, the turbojet engine may be producing a small amount of thrust with large changes in RPM, but near the upper operating limits, very small changes in RPM produce big changes in thrust.
Yes indeed, turbojet engines change speed in order to alter their thrust. The lower end is the idle speed, which usually changes from ground to flight...flight idle speeds are a little higher, and is typically about 50 to 60 percent of the maximum engine RPM. Cruise RPM is typically about 90% of the maximum RPM.
RPM may, or may not be the measurement used to determine what the engine is doing, however. Unlike a turboprop engine where the primary power instrument is the torque gauge, a turbojet engine may use RPM, or may use EPR...a measurement of the pressure difference between what's coming out the back of the engine and what's going in the front. This only measures the engine core thrust, however, and doesn't address what a turbofan is contributing with the fan section...that part is read on the N1 gauge, which is a measurement of one part of the RPM of the engine...not necessarily the RPM of the engine as a whole.