\( \int \frac{\left(\sqrt{1+x^{2}}+x\right)^{10}}{\left(\sqrt{1+x^{2}}-x\right)^{9}} \, dx = \frac{1}{m}\left(\left(\sqrt{1+x^{2}}+x\right)^{n}\left[n\sqrt{1+x^{2}}-x\right]\right)+C \)
If where \( C \) is the constant of Integration and \( m , n \in \mathbb{N} \) then \( m+n \) is equal to ______________.
