Such power? Much scare! Many wow!

Algebra Level 5

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 $a-2b$ ?