Let's do some calculus! (33)

Calculus Level 5

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

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 \(a+b+c\).

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