You have the following function:
y = ∛(x - 1)
remind that the domain are the values that allows the function y is a real function, in this case, due to the index of the root is odd, there is not restriction in the values of (x - 1), becasue the cubic root of a negative or positive number is a real number.
Hence, the domain are all real numbers.
-∞ < x < ∞