I know about Abel–Ruffini theorem, but I have a polynomial of special form. From "Beyond the Quartic Equation" by R.B. King (a very interesting book, btw) I've learned about Tschirnhaus transformations which I try to use, to convert my polynomial 
$$
x^9 +  ax^6 + bx^5 + cx^3 + d = 0$$
to the form 
$$
x^9 +  ax^6 + bx^3 + c = 0,
$$
so I could do substitution $t = x^3$ and use Cardano's formulas. What other things I can try? 

I would prefer solution in radicals, but closed form solution with elliptic functions will also be satisfying.