Irrational Exuberance

Calculus Level 3

$\large{ f(x) = \begin{cases} x^2 , \quad \text{ rational }x \\ x^3 , \quad \text{ irrational }x \\ \end{cases} }$

Let $f(x)$ be described as the function above. If $f(x)$ is continuous at exactly $p$ points and differentiable at exactly $q$ points, find $p+q$ .