Nonlinear Systems & Linearization · Hard problem

A system has $x$-nullcline $y = x^3 - 6x^2 + 11x - 6$ and $y$-nullcline $y = 5x - 6$. These curves cross at three points, giving three equilibria. Without solving for the equilibria individually, use Vieta's formulas on the resulting cubic to find the sum of their $x$-coordinates.