Let the ordered triples $(x,y,z)$ of complex numbers that satisfy \begin{align*} x + yz &= 7, \\ y + xz &= -3, \\ z + xy &= -5. \end{align*} be $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\dots,$ $(x_n,y_n,z_n).$ Find $x_1 + x_2 + \dots + x_n.$
+1348 
