Partial Derivatives & the Gradient · Challenge problem

For constants $a$ and $b$, let $f(x,y) = \dfrac{3x^3 + a\,xy^2 + b\,x^2y - y^3}{x^2 + y^2}$ for $(x,y) \ne (0,0)$, and $f(0,0) = 0$. There is exactly one pair $(a,b)$ for which $f$ is differentiable at $(0,0)$. Find $a + b$.