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

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 $\sqrt{a+b}$.