Find x ∈ R such that (∛17)^√(55-√x) = 289

This nested radical exponent equation was motivated by a slightly easier version of it created by math teacher @silverlining1999 from a surds and indices lesson. The irrational base is quite easy to handle with properties of exponents.
Motivational speaker/writer and Trumpeter Philip Lloyd deplores memorization it appears while ensuring his students understand why B^0 = 1 for all real B other than B=0
Pablo Emanuel was mistaken when he declared "First of all, there are no truly rational numbers in real life" This means Pablo never drank a cup and a half of coffee I guess?! 1.5 = 3/2 a nice healthy rational number. The mathematician might counter that 3/2 was just an estimate for the coffee consumed, but that could be countered by 1 cup is also just an estimate AND then we would have to conclude there are no "truly integer numbers in real life" These type of reality debates always hinge on what philosophy interlocutors mean by "real life"