That is indeed a nice feature of types: You can overload notions. In this case you overload the notion "principal cube root" (PCR) to mean different things for ℤ and for ℂ.
But really, "principal cube root" as you would like it to behave is not well-defined just for a number, you also need to provide the algebraic structure you consider it in, as in PCR(ℤ, -1) = -1, and PCR(ℂ, -1) = (1 + sqrt 3) / 2.
Alternatively, just set PCR(-1) = (1 + sqrt 3) / 2. That makes probably the most sense, as there is not much value in a PCR notion for integers in the first place.
But really, "principal cube root" as you would like it to behave is not well-defined just for a number, you also need to provide the algebraic structure you consider it in, as in PCR(ℤ, -1) = -1, and PCR(ℂ, -1) = (1 + sqrt 3) / 2.
Alternatively, just set PCR(-1) = (1 + sqrt 3) / 2. That makes probably the most sense, as there is not much value in a PCR notion for integers in the first place.