# Shourya's non-real roots

Algebra Level 5

For each real number $r$, let $X_r$ denote the sum of all non-real roots of the equation $128y^4-128y^3+64y^2-16y+r=0$. Let $S$ be the sum of all possible distinct values of $X_r$. Given that $S$ can be written as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers, what is the value of $a+b$?

This problem is posed by Shourya P.

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