Does the cube root of 1 equal +-1 or just 1--->x^3=1?

Answer 1

it is only +1, since (-1)^3 = -1, not 1.

Answer 2

x^3 = 1
x^3 - 1 = 0
(x-1)(x^2 + x + 1) = 0
x = 1 or x = (-1 ± √-3)/2 = (-1 ± √3 i)/2 two complex roots

so x = 1 as a real solution.