Don't use quadratic equation

Algebra Level 3

If \(x-y=8\) and \(x^2+y^2=80\) ,then \(x^{-3}-y^{-3}=z\).

If \(|z|=\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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