Product of Years

Algebra Level 5

\[ \large (x + 2010)(x + 2011)(x + 2012)(x + 2013) = 5 \]

If the maximum real value of \(x\) such that the above equation is true can be expressed in simplest terms as

\[ \large \frac{\sqrt{a+ b\sqrt{c}} -d}{e}\]

For positive integers \(a,b,c,d,e\) with \(c\) square-free, and \( \gcd (a,e) = 1 \).

Find \(a+b+c-d +e\).

This problem is not original.

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