Usually Maple gives solutions in terms of radicals only up to degree=4
(for example using RootOf + allvalues).
Using 'irreduc' (to test first) and 'galois' (to check for the Galois
group, if degree <= 9) I have cases, where the result implies, that by
theory the roots can be given through radicals:
Though the results are difficult to read in my case they are 'C(6)' or
'C(8)', the cyclic groups of that order - thus abelian and IIRC those
groups are solvable.
