Solve this if you can!

Let $x+y = \zeta$ . From the equation expansion, we will get $\zeta^2 = 85+2xy$ and $\zeta^3 = 737+3\zeta xy$ . Writing $xy$ in second equation in the terms of $\zeta$ gives $xy = \frac{\zeta^2-85}{2}$ . Substituting this in the third equation gives $737+3\zeta(\frac{\zeta^2-85}{2}) = \zeta^3$ Simplifying to $\zeta^3-255\zeta+1474 = 0$ or $(\zeta-11)(\zeta^2+11\zeta-134) = 0$ . Solve for integer, $\zeta = 11$