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I'm trying to figure out a trick to finding the degree of

(81)^1/5+29(9)^1/5+17(3)^1/5-16 over Q.

I know that the degree of this number, call it a, is equal to the degree of the field extension

[Q{a}:Q], and also the degree of the minimal polynomial which has this as a root. Unfortunately, I can't seem to find an answer for it.