Use scipy.optimize.brentq to find the solutions to the equation
$$
x + 1 = -\frac{1}{(x-3)^3}
$$
Rewrite the equation as $$ f(x) = x + 1 + (x-3)^{-3} = 0. $$ This function is readily plotted and the roots may be bracketed in $(-2, -0.5)$ and $(0, 2.99)$ (avoiding the singularity at $x=3$).
In [x]: f = lambda x: x + 1 + (x-3)**-3
In [x]: brentq(f, -2, -0.5), brentq(f, 0, 2.99)
Out[x]: (-0.984188231211512, 2.3303684533047426)