\[\large \left( 1 + \dfrac{x}{1!} + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \ldots + \dfrac{x^n}{n!} \right )^2 \]

For \(n\geq 6\), if the coefficient of \(x^6\) in the expansion above can be expressed as \(\dfrac{a}{b} \) for coprime natural numbers \(a,b\), find \(\sqrt{a+b} \).

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