Consider \[ I = \frac{1}{2\pi i} \int_C \frac{\sin z}{1 - \cos(z^3)} \, dz, \] where \( C = \{ z \in \mathbb{C} : z = x + iy, |x| + |y| = 1, x, y \in \mathbb{R} \} \) is oriented positively as a simple closed curve. Then, the value of \( 120I \) is equal to _________ (in integer).