The curve satisfying the differential equation  $\left(2x^{2}y-2y^4\right)dx+\left(2x^3+3x{y}^3\right)dy=0$ and passing through $\left(1,1\right)$  is given by $2\ln \left(xy\right)+\frac{y^m}{x^n}=1,$$\left(m,n\text{\hspace{0.33em}}\in N\right)$   , then the value of  $m+n$ is