You can use it for receiving on any band, of course.
Generally, antennas may work on third harmonics. For example, 2m and 70cm are close third harmonics.
Sometimes they work on second harmonics (i.e., 10m and 20m), especially dipoles.
So your 60m antenna may work on 30m and 15m.
If you have an antenna tuner (or one is built into the radio), you might be able to operate it all band, but you may have high SWR and common mode current in the feedline. High SWR without a tuner can damage the radio; high SWR with a tuner will incur large losses in the feedline, but might work anyway. Common mode current can be partially suppressed at low power with a balun, sometimes built into the antenna. The danger of common mode current (besides typically higher SWR) is RF radiated directly from the coax, possibly in the shack and on the chassis of the radio. (Watch out for RF burns.)
Also, you could create a fan dipole to get additional bands.
If you don't have an antenna analyzer, you should at least have an SWR meter built into the radio. You can operate on a mismatched antenna at low power (1w or less preferably, up to 5w maybe) without damaging the radio. (High SWR may make the radio arc internally short term and overheat long term.) Most radios have a TUNE button for this purpose. Check the manual on your radio to be sure what power it uses. If you don't have a tune button, you can use a CW key and put out a test pulse. Start at the lowest possible power and watch the SWR meter, and raise it slowly to make sure the SWR doesn't increase when you put out more power. Remember, the SWR the radio sees may be lower than the real SWR because of loss in the transmission line. An SWR below 1.5 is typically considered good with negligible loss. Most solid state radios can tolerate an swr of 2 or lower. Most tube radios can tolerate an swr of 10 at 100W. Tuners may also be able to take swr of 10, but may arc internally at higher swr or higher power depending on the tuner.