\[\begin{cases} a^2+b^2+c^2+d^2+e^2 = 25 \\ a+2b+c+ d \sqrt{3}+e = 13\end{cases} \]

If \(a,b,c,d\) and \(e\) are real numbers satisfying the two equation above, find the sum of the minimum and maximum possible values of \(e\).

If you got your answer as \(\dfrac{A}{B}\), where \(A\) and \(B\) are coprime positive integers, submit your answer as \(A\times B\).

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