No, I'm not talking about becoming very drunk.
Apportionment of Representatives is based on the Census, counting the whole number of persons in each State, excluding Indians not taxed.
Now, remember the history behind the "three fifths" language formerly included. 'Twasn't that the Founders all thought that a Black was worth only 60% of a White; oh, no. The slave-holders wanted slaves (those "all other persons") counted fully; the abolitionists didn't want them counted at all.
Because, of course, slaves didn't have the vote, so any representation based on their numbers would actually be representing their owners. Own more slaves, get more representation for the enfranchised men of your district.
Consider the situation right now, here in Silicon Valley. A substantial (and growing) fraction of the population is non-citizen guest workers. Now, what does the 14th Amendment have to say about them? Right. Nothing. It says nothing about citizens, eligible voters, none of that: just the whole number of persons. (Many of the guest workers are in fact Indians, but not that kind, and they are taxed).
So... they don't have the vote, but their presence here is counted for purposes of apportionment. The plantation owners fulfill their ancient wish, and get the full measure of extra representation for every serf toiling in their cubicle farms.
Oh, and it's the same deal with illegal immigrants, to the extent that the Census can find them. No vote, but extra representation for those who do have the vote.
... dissolve the People and elect another, anyone?