Find the real number coefficient $c$ of polynomial $x^2+x+c$, if his roots $x_1$ and $x_2$ satisfy following: $$\frac{2x_1^3}{2+x_2}+\frac{2x_2^3}{2+x_1}=-1$$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011
Tags: algebra, polynomial