Find the isolated singularities of the function and calculate their residues

Question

Find the isolated singularities of $\dfrac{3z}{z^3+1}$ and calculate their residues using the 'g/h rule'

I understand that $z=-1$ is a singularity but I'm not sure about the others or how to apply the gh rule to this function.

Answer 1

HINT:

$$z^3=-1\implies z^3=e^{i(2n-1)\pi}$$

for $n=0,1,2$.

Alternatively, write $z^3+1=(z-1)(z^2+z+1)$ and find the roots of the quadratic.