let's solve this normally

x^3 + 1 = 0

=> x^3 = -1

=> x = (-1)^(1/3)

the real solution is of course, -1. since (-1)^3 = -1

there are no complex solutions to this as far as i can tell, unless we want to make things complicated and do something like i^(2/3), that way, (i^(2/3))^3 = i^2 = -1, and we could try to come up with a formula for all fractional powers of i that causes this to happen, but that's just overkill as far as i'm concerned