Let the roots of the polynomial $2x^{3}-3x^{2}+5x+c$ (where $$c$$ is a constant) be $$\alpha$$, $$\beta$$, and $$\gamma$$. If $\frac{1}{\alpha\beta}+\frac{1}{\alpha\gamma}+\frac{1}{\beta\gamma}=\alpha\beta+\alpha\gamma+\beta\gamma,$ then the value of $$c$$ can be written as $$-\frac{m}{n}$$, where $$m$$ and $$n$$ are positive, coprime integers. Find the value of $$m+n$$.