Visualize a projective curve $X^3+Y^3=Z^3$ in $P_2(C)$ as a torus

Question

Let $P_2(C)$ be the 2 dimensional complex projective space, I want to prove that the projective curve defined by $M=\{[X,Y,Z]\in P_2(C)|X^3+Y^3=Z^3\}$ is a torus. I know that there is a theorem saying that its genus is C(3-1,2)=1 but I'd like to visualize that by constructing the Riemann surface of the multi-function $y^3=1-x^3$. I can prove that on the Riemann sphere $S$, except 3 points $\{[1,1], [\omega, 1], [\omega^2,1]\}$ where $\omega^3=1$, all other points has 3 pre-images under the map $f: M \rightarrow S$ defined by $f([X,Y,Z])=[X,Z]$. Then I'm stuck: how to cut and glue the 3 spheres to become a torus, based on the 3 points?