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Algebra Level 4

\[ \large \prod_{k=1}^{2015} \frac{k^2 + k}{k^2+5k+6} \]

If the product above can be written as \( \left(a^4 \times b \times c \times d \times e^2 \right)^{-1} \) for distinct primes \(a,b,c,d,e\), evaluate \(a+b+c+d+e\).

You may use the List of Primes as a reference.

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