when I open the addonmanager option in the fsx, I only find on the right side a list of manufactures and airport enhanced I guess
I guess your confusion comes because it's seems you have assumed the Addon Manager is a "GSX menu". It's not. It's a menu that can be used to purchase, activate and deactivate a number of products, not all from FSDT, but from other developers that use it too.
So, those are not the airports "enhanced" by GSX, they are just airports you can buy from us or Flightbeam, or Cloud9.
The ONLY section relevant to GSX in that menu, is the GSX entry so, in order to activate, you must click on GSX first, and the press the "Register Serial" button, and insert your GSX Serial Number. This is of course explained in the GSX manual, at Page 4:
Very briefly, activation it’s done this way:
Open the “Addon Manager” menu inside FSX, under the “Addons” menu
Select Fsdreamteam and GSX in the two small text windows
Click the “Register Serial” button
Type your Serial Number, as indicated in your purchase receipt
Let it activate, with a working internet connection
The program will also prompt you with the first starting letters, so it's not that you can confuse it with something else.
Note that, if you have a firewall/antivirus which is blocking access to the activation server, you might have to do a Web-based activation.
In THIS case, insert the Serial Number ONLY in the "Register Serial" dialog, and DO NOT confuse it with the "Installation ID" which is being asked by the Web page. The installation ID (if you are activating on the same computer) it's already correct and pre-filled: there's nothing to type there, just press the "Submit" button and wait for the Activation Key which will have to be inserted back in the sim.