Expressing the solution to a rational expression in radical form

Question

I'm trying to find the solution to this equation

$$ -\frac{3}{r} + \frac{8}{r^3} = \frac{\sqrt{2}-1}{2} $$

but I haven't been able to find a solution in radical form. Although I've found the solutions as decimals, I am looking for a solution in radical form. What are the solutions to this equation expressed as radicals?