Consider cases. Obviously, x cannot equal zero, or you'll have division by zero.
If x > 0, then |x| = x, and you have 1 + x > 6/x, so x^2 + x - 6 > 0.
If x < 0, then |x| = -x, and you have 1 - x > -6/x, so 0 < x^2 - x - 6.
Solve the two quadratic inequalities.