# $$P(\sqrt[3]{x})$$ won't work here

Algebra Level 5

A polynomial $$P(x)$$ is defined as $P(x)=2x^3+3x^2+5x+1$

If the roots of $$P(x)$$ are $$p,q,r$$, then the value of $p^3q^3+q^3r^3+r^3p^3$ can be expressed as $$\dfrac{a}{b}$$ for positive coprime integers $$a$$ and $$b$$. What is $$a+b$$?

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