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The roots of the cubic equation

$x^3 - 4x^2 + 6x - 5 = 0$

are $p,q,r$. If

$\large \frac {p^3}{q^4+r^4} + \frac {q^3}{p^4+r^4} + \frac {r^3}{p^4+q^4} = - \frac {a}{b}$

for coprime positive integers $a,b$. What is the value of $a-2b$?

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