filtering – How to select p terms with powers larger than 1 in a given expression?

My expression is:

$expr = frac{p^{frac{1}{3}} q + 5}{3q^2} + p^2 + (p -1)^{frac{1}{3}}$

And I want to single out all terms with $p^k, k > 1$

How should I do that? (If there is any way other than applying Series() would be the best, since I want it to be less time-consuming when dealing with large expr.)