Find the smallest constant C such that for every real polynomial $P(x)$ of degree 3 that has a root in the interval $[0,1]$, $$\int_{0}^{1} \left\vert P(x)\right\vert\, {\rm d}x\leq C\max _{x \in[0,1]} \left\vert P(x) \right\vert$$. The original answer is in \frac{m}{n} format, please give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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