$\large {( x+y )}^4 = x-y$

Real numbers $x$ and $y$ satisfy the equation above.

The maximum value of $y$ can be expressed in the form of $\dfrac{a \sqrt[3]{b}}{c}$, where $a$, $b$ and $c$ are positive integers, with $a$ and $c$ being coprime integers and $b$ a prime.

Submit your answer as $a+b+c$.