Let's do some calculus! (33)

Calculus Level 5

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

Real numbers xx and yy satisfy the equation above.

The maximum value of yy can be expressed in the form of ab3c\dfrac{a \sqrt[3]{b}}{c}, where aa, bb and cc are positive integers, with aa and cc being coprime integers and bb a prime.

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

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