Solving $a=x^p - (x-b)^p$ for arbitrary $a,b$, and $p$ being natural/rational?

I encountered the following equation:
$a=x^p – (x-b)^p$

that i want to solve for $x$ and for a general choice of parameters $a,b,p$.
I am wondering if it is even possible to solve the above equation analytically without specifying the exponent $p$. And even if the equation can be solved for $p$ being a natural number, can this be also done for a rational $p$.