How to control any MIDI parameter in Ableton Live from a Max patch ?

Hello, I've been through a bunch of topics about this but still can't figure how to make it work... Basically I wish I can control any assignable MIDI parameter in Live (those in purple when clicking MIDI button) from a patch within Max (and NOT M4L).
I think I route things correctly ('from Max 1'.....), I can use perfectly noteout in Max to play synths in Live, but can't control any parameter that appear in purple in Live midi map mode. I saw in some topics that one could be able to select a fader in Max connected to a ctlout object after selecting the desired purple parameter in Live (like one would proceed to assign an external MIDI controller) but it doesn't work for me. Moreover, when trying to send a parameter via ctlout, I can see that Live receives a MIDI signal (yellow blinking) but nothing else happens.
That said I don't really understand how ctlout works since I don't know how to assign it to any particular parameter in Live, and the documentation just confuses me...
Thanks for your help !