A calculator cannot take the regular cube root of a negative number.

To get the right result, make the expression positive first, then take the cube root, and then add the minus sign again.

The "i" you got is the so calledimaginary number.

It is a correct result, but it takes you out of the world of the real numbers into the so calledcomplex numbers.

In particular, the cube root has multiple values when extended to the complex numbers.