I find geometry a bit interesting

Geometry Level pending

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 \(a + b + c + d + e\).

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