A long limit

Calculus Level 5

The value of the limit

\(L=\displaystyle\lim_{y \rightarrow \infty} \sqrt[7]{(8y+3)(y+1)(y+2)(y+3)(2y+3)(2y+5)(4y+5)}-2y\)

is of the form \(\dfrac{A}{B}\) where\(A\) and \(B\) are co-prime integers.

Find the value of \(A+B\).

\(\textbf{Note :}\) Do \(\textbf{NOT}\) use wolfram alpha.

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