Differential Equations · Challenge problem

The initial value problem $\dfrac{dy}{dx}=3y^{2/3}$, $y(0)=0$ has the trivial solution $y=0$, but also non-trivial solutions of the form $y=(x-k)^3$ for $x\ge k$ (and $y=0$ for $x<k$). If such a solution satisfies $y(3)=1$, find $k$.