It is given that \(x,y\in\Bbb{Z^+}\) and they satisfy the equation given below:

\[\large\prod_{k=0}^5\left(5^{2^k}+6^{2^k}\right)=6^x-5^y.\]

What is the value of \(x+y?\)

\(\)

**Note:** This problem is not original. It is adapted from a question posted on Math SE.

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