Calculate rotor slip without knowing synchronous speed
The rated speed is usually about 90-95% of synchronous speed. You can guess the synchronous speed and number of poles by looking for a number of poles that gives a rated speed slightly less than synchronous speed.

In this case, I would guess you are dealing with a 60Hz 12-pole motor, which would have a synchronous speed of 600 rpm.

I've done a quick lookup table below for reference.

Poles    50hz    60hz
2        3000    3600
4        1500    1800
6        1000    1200
8        750     900
10       600     720
12       500     600
16       375     450
20       300     360
24       250     300
30       200     240
40       150     180