I get you can incorporate them however you want into your own writing... but what about when playing with others? For example, if the chart of a song has a IV chord, would a I11 chord work over the IV in most situations? If you throw a major 6th into a I11 chord, that would esssentially make it a IVmaj9.
where i come from, "11" usually only is used on minor chords. i don't quite see how your example adds up. in C assuming you mean 1,3,5,7,9,11 (which mostly no one would do, i'm not sure if you meant#11? or is it a minor chord all along?) and then you add a 6, that doesn't really make Fmaj9. anyway, it's not too good to think about it this way. just use the notes you need to support the melody, then afterwards you can argue about what to put on the page. Sounds like you are a bit goal oriented on using the number 11 on the page, and that might not be a good way to look at it. A useful example of something that might end up being called "11" is let's say it's the key of C, melody note is G, and it's a Dmin7 chord. in reality you might play C,F,G(notes) in the chord, and call it Dmin11 if you want. Or let's say you are in the key of Cmin and it's just a Cmin vamp for a while and you've got a melody that is focusing on the F note. then you might use F,D,Bb notes in your chord, with the Eb tucked in there too. or more likely even, oscilating between a Bb triad and Eb triad in the chord. similarly in the relative major version of that, in the key of Eb, you might see a F note on a Cmin chord, and the chordal player will play Bb triad (over C) first, before swicthing to the Eb triad (Cmin7). all these things might be called 11. but to be honest it's not too necessary to really use the number 11 when talking about chords, it's kind of confusing, and the way it's taught as a stack of 3rds up to 11 is a bit confusing and does not really represent most musical realities. because a full stack up to 11 would have 6 notes, and most chords have less than 6 notes, so most chords being called '11' wont really have all the notes. also stacking it from the bottom up is not something that normally happens in reality outside of a music textbook or class. usually when you see 11 on the page it just means that the melody note is a 4th above the bass. and the remaining notes are chosen sensibly for the situation. i hope that makes sense