There is not really a minimal height.
We must try to do our upmost and deal with what we can.
The thing is...horizontal antennas bennefit from a thing called "ground gain" in a better way then vertical antennas do...at least...when they are at a sufficient height above ground.
Now the "turn over point" is roughly about 6-7 meters. (for CB ...not 20/15/10)
So...your first priority would be to get the horizontal antenna at least 7 meters of the ground....if you cant it is better to focus on a vertical beam (quad)
Verticals will provide more gain under a low angle in that case.
(again ...the above is "roughly")
Now...if you have reached that height, you can easilly improve your DX capabilities by putting the thing up higher.
Going from 7 to 11 is most certainly worth the effort, going higher too....
But then your going into the mechanically issues.
With that said....sunspots are dropping....low angle will become more important
And if your really into working that special "DXCC" you will end up asking for higher...higher and bigger time after time.
If your into "o whell i just spoke to a guy across the pond" without a doubt that 11 meter with a Sirio SY-4 will get you there many many times...heck...such a setup is allready more than most have, and will put you in a nice "DX" position.
Hope it is of use,
Kind regards,
Henry 19DX348