Singularities on a weighted projective curve

Question

Let $C$ be the curve of degree $3$ defined over $\mathbb{C}$ given by $$x(y+z)=y^3-z^3$$

which lives in the weighed projective space $\mathbb{P}(x,y,z)=\mathbb{P}(2,1,1)$.

Is the curve singular ?