One of the points of intersection of the curves $y=1+3x-2x^2$ and $y=\dfrac{1}{x}$ is $\left(\dfrac{1}{2},\,2\right)$. Let the area of the region enclosed by these curves be $\dfrac{1}{24}\big(l\sqrt{5}+m\big)-n\ln(1+\sqrt{5})$, where $l,m,n\in\mathbb{N}$. Then $l+m+n$ is equal to: