I didn't think it was a question to ask...you are correct it is a Eb7add6... 
The general concept of building chords is this:
Start with the root and add thirds, then alter each note (aside from the root) up or down a half-step to create the desired tonality.
Hence, 1, 3, 5, 7, 9, 11, 13. By altering or excluding any note (aside from the root) or combination of notes, we can create any possible chord.
When we talk about chord extensions we are talking about 9ths, 11ths, and 13ths. 2nd, 4th, and 6th fit into scale theory as in 1, 2, 3, 4, 5, 6, 7.
Think of chords as stacked:
13
11
9
7
5
3
1
Think of scales linearly:
1 2 3 4 5 6 7
Extensions are after the fact, hence using a number below 7 conflicts with this idea.
In my opinion, what it really comes down to is this - Will everyone interpret my chord symbol the same? I think the following are all acceptable as I don't think there is any other way to interpret them except Eb, G, (Bb), Db, C:
Eb7(6)
Eb7(add6)
Eb7(13)
Eb7(add13)
As to which one I prefer, it's Eb7(13), simply because using a 6 doesn't fit well with the concept of adding extensions (extensions are above the 7th).
A favorite quote of mine is, "Music theory is just a theory, just like evolution is a theory". A theory is what we use to explain what we see in nature. A theory is not a law until it is proved over and over again with the scientific method. Every theory has holes. Classical music theory is how classical musicians relate their experience, the same goes for Jazz theory, etc. There are as many music theories as there are musicians. I prefer Jazz theory, but of course I probably have my own twist on it. Theory is about communication.
So why did I bother correcting the chord symbol? My approach should have been, "I prefer calling it a V7(#5,#9), because..." I only try to correct chord symbols if I think they create ambiguity in my mind. It is very subjective, but it goes back to communication. If we don't talk about it, then we'll never reach a concensus upon a "least ambiguous" theory that allows for effective communication.
Sorry for hijacking your thread Danati, I didn't realize where this would lead! LOL
