Let's try counting the number of perfect squares and cubes less than $ 441=21^2 $. There are twenty perfect squares less than 441: $ 1^2, 2^2, \ldots, 20^2 $. There are also seven perfect cubes less than 441: $ 1^3, 2^3, \ldots, 7^3 $. So there would seem to be $ 20+7=27 $ numbers less than 441 which are either perfect squares and perfect cubes. But wait! $ 1=1^2=1^3 $ is both a perfect square and a perfect cube, so we've accidentally counted it twice. Similarly, we've counted any sixth power less than 441 twice because any sixth power is both a square and a cube at the same time. Fortunately, the only other such one is $ 2^6=64 $. Thus, there are $ 27-2=25 $ numbers less than 441 that are perfect squares or perfect cubes. Also, since $ 20^2=400 $ and $ 7^3=343 $, then all 25 of these numbers are no more than 400. To compensate for these twenty-five numbers missing from the list, we need to add the next twenty-five numbers: 401, 402, $ \ldots $, 424, 425, none of which are perfect square or perfect cubes. Thus, the $ 400^{\text{th}} $ term is $ \boxed{425} $.