Laplace inverse, using inversion formula

Question

I need to find the Laplace inverse of $$\frac{1}{p^3+1}$$ I have found it using partial fraction decomposition and checked it to make sure my answer was right, so I know the correct solution. I wanted to try and compute it directly using the inverson formula, but can't seem to get the same answer, I end up with a residue of $\frac{e^x}{3}$ and the final answer is different from the correct answer. Any help will be appreciated!