I have a problem how to solve this irrational equation. It is important to note that it is not necessary to present roots in radical form (impossible). For me it is important to have roots in this form for example

x == Root[19 - 22 #1 + #1^5 &, 1]...

I am not sure how to find list of coefficients for alternate form of the poly equation if it is exist. Equation is in the following form:

 eq = Sqrt[
 Sqrt[Sqrt[(x + 1)^7] + Sqrt[(x*a + b)^3]] + Sqrt[
 Sqrt[(x + 1)^4] + Sqrt[(x*a + b)^3]]]/Sqrt[
 Sqrt[(x*c + 1)^3] + Sqrt[(x*d + a)^5]];

 Solve[eq == 0, x]

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