One of the points of intersection of the curves $y=1+3 x-2 x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by these curves be $\frac{1}{24}(\ell \sqrt{5}+\mathrm{m})-\mathrm{nlog}_{\mathrm{e}}(1+\sqrt{5})$, where $\ell, \mathrm{m}, \mathrm{n} \in \mathrm{N}$. Then $\ell+\mathrm{m}+\mathrm{n}$ is equal to