\(P(\sqrt[3]{x})\) 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 \(a,b\). What is \(a+b\)?

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