The ilaplace function of the symbolic engine currently does not implement an explicit expression for
ilaplace(1/(5 + (3*(s^a + (1/2^a)))/(s^a + (1/6^a)))) if a is not an integer .
The ilaplace function computes the analytic closed inverse Laplace form of a transfer function. It seems that mathematically a closed inverse Laplace form for 1/(5 + (3*(s^a + (1/2^a)))/(s^a + (1/6^a))) for general a cannot be found out, so ilaplace function will not simplify it further.
Nevertheless, there is a community submission at MathWorks File Exchange which numerically approximates an inverse Laplace transform for any function of "s". Following is the link of the same:
