>>106916640
That only applies for even numbered roots.
If you have y = x^2, it can take negative and positive number inputs and give out positive number outputs. Its inverse, y = ±sqrt(x), is the opposite, it takes in positive number inputs and gives out negative and positive number outputs. But you have to add that ± symbol because y = sqrt(x) only gives out positive outputs, and this is because of the definition of a function (one input should only have one output).
So, when you have x^2 = 1, and you apply its inverse to both sides: ±sqrt(x^2) = ±sqrt(1) => x = ±sqrt(1) => x = ± 1.
But with odd numbered roots, this doesn't apply.
If you have y = x^3, it can take negative and positive number inputs and give out negative and positive number outputs, so its inverse, y = cbrt(x), can also take in negative and positive inputs and give out negative and positive outputs. This means that there's no need to add a ± symbol.
I over-explained because I'm a retard, and that's how i understand it. In practicality, x^2 - 1 = 0 has two numbers that satisfy the equation: positive and negative 1, and x^3 - 1 = 0 has only one number that satisfies the equation: positive 1.
