If ∫ ((√(1+x^2)+x)^10)/((√(1+x^2)-x)^9) d x=1/(m)((√(1+x^2)+x)^n ( n √(1+x^2)-x))+ C where C is the constant of integration and m, n ∈ N, then m + n…

If $\displaystyle \int \frac{\left(\sqrt{1+x^2}+x\right)^{10}}{\left(\sqrt{1+x^2}-x\right)^9} \mathrm{~d} x=\frac{1}{\mathrm{~m}}\left(\left(\sqrt{1+x^2}+x\right)^{\mathrm{n}}\left(\mathrm{n} \sqrt{1+x^2}-x\right)\right)+\mathrm{C}$ where C is the constant of integration and $\displaystyle \mathrm{m}, \mathrm{n} \in \mathbf{N}$, then $\displaystyle \mathrm{m}+\mathrm{n}$ is equal to $\displaystyle \_\_\_\_$.