Numbers are starting to look fuzzy again...

So, I have this practice problem:

$\displaystyle x^\frac{1}{2} - 3x^\frac{1}{3} = 3x^\frac{1}{6} - 9$

I was able to get the root x=27

$\displaystyle x^\frac{1}{3}(x^\frac{1}{6} - 3) = 3(x^\frac{1}{6} - 3)$

$\displaystyle x^\frac{1}{3} = 3$

$\displaystyle x = 27$

However, the book indicates that there are two roots: x = 27 and x = 729. I confirmed this with my calculator, but I am wondering how I was supposed to have figured out that other root. What did I miss here?