I find geometry a bit interesting

Let the equation $x^{3} + y^{3} + 3xy = 1$ represents the co-ordinate of one vertex $A$ and the equation of a side $BC$ of the triangle $ABC$ .

If locus of centroid of triangle $ABC$ is $ax^{3} + by^{3}+ cx^{2} + dx + ey + f = 0$ . Then find the value of $a + b + c + d + e$ .