For real numbers x, y, z such that x ≠ y ≠ z, \(\left|\begin{array}{lll} x & x^{2} & 1+x^{3} \\ y & y^{2} & 1+y^{3} \\ z & z^{2} & 1+z^{3} \end{array}\right|\) = 0 and \(\left|\begin{array}{lll} 1 & x & x^{2} \\ 1 & y & y^{2} \\ 1 & z & z^{2} \end{array}\right|\) ≠ 0 then xyz = _______.