What is the sum of values of $x$ ?

since $x^3 + 0 \cdot x^2 - 1 = 0$ , so according to Vieta's formula: $\sum root_i = \dfrac 01 = 0$

Complex multiplication is to increase the angle and multiply the distance. Therefore $\newline x_1=\LARGE{1},$ $\newline x_2=\cos \frac{\tau}{3} + i \sin \frac{\tau}{3} \newline = -\frac{1}{2} + \frac{\sqrt{3}}{2}i \newline = \LARGE{\frac{-1+\sqrt{3}i}{2}},$ $\newline x_3=\cos \frac{\tau}{3} + i \sin \frac{2\tau}{3} \newline = -\frac{1}{2} - \frac{\sqrt{3}}{2}i \newline = \LARGE{\frac{-1-\sqrt{3}i}{2}}.$ $\newline x_1+x_2+x_3=1+\frac{-1+\sqrt{3}i-1-\sqrt{3}i}{2} \newline = 1+\frac{-2}{2} = \LARGE{\boxed{0}}.$