How can I solve this integral? I worry about the exponential function, normally I would just use the residue theorem but here I worry it is not possible to use it.
$$\LARGE\oint\frac{e^{i\sqrt{\frac1z+z+1}}}{-z^2+z+1} dz$$
The contour is a unit circle $|z|=1$. Any help would be appreciated.