A Chebotarev-free argument is given by our own @Pete L Clark here:
https://math.stackexchange.com/questions/6976/proving-that-an-integer-is-the-n-th-power
A Chebotarev-free argument is given by our own @Pete L Clark here:
https://math.stackexchange.com/questions/6976/proving-that-an-integer-is-the-n-th-power