Your question is a little "loaded" as there are many different air coolers out there, some of which rival water coolers. I personally don't own a FX 6300, but the best overclock I've done on one for a customer was 5Ghz (multiplier only), I don't remember the Vcore, but I won't sign off on an overclock if its over 1.5V so it was at or under 1.5V and that was using an NH-U14S air cooler.
Now with my FX 8370 my very best overclock was 5.5Ghz (multiplier only) @ 1.55V (jumping to 1.6V under full load). Wasn't comfortable with the voltage for everyday use so scaled it down to 5.05 (23.5 base clock 214 BUS) @ 1.46V (under full load hitting 1.476V). Of course I also have a NH-D15S with 3 fan configuration, but it is "on air". If I were you I would be very careful with 1.56V as depending on your LLC settings you could easily be hitting over 1.6V under full load which is potentially very dangerous. I would run a stress test like Prime 95 with a monitoring program like HWmonitor running in the background. Let the stress test run for about 20 minutes and check to see what your highest recorded Vcore was. Really the maximum safe Vcore for an FX chip is 1.55V, and I would be willing to bet that your hitting over 1.56V under full load stress testing.