The dominant eleventh chord, just like the fourth chord, can be constructed stacking fourth intervals and has the same openness to it's sound. However, it does want to resolve to a seventh chord. Mainly because the 11 (also the suspended fourth) wants to resolve down to the major third. As such, it is also used in this way. C11 to C7.
This specific version of the chord also has a ninth because writing an 11 (or any extended note above the octave) explicitly signifies that all the extended notes under it are also included. You could very well play it without the ninth. This would make it to behave more like a C7sus, which on it's own resolves just the same way as C11.
Usage and play
This chord is mostly used in Jazz and Classical music. However you might occasionally find it in Pop songs.
The main way of using this chord is as stated above: By resolving the perfect fourth (or 11) downwards to a major third you release the bit of tension created.
Fun Fact: on a guitar you can play the 11-chord by plucking all the strings except the low E without using your left hand!
Interestingly enough, just like it's little brother (the fourth chord) you can continue playing this on quite some chord-degrees. Although some might create a bit more dissonant notes and should be used with more care.
Playing in E minor, you would have these chords (with their respective notes in the correct order), where A would contain the eleventh chord:
Em7/11 (on guitar, all open strings!) - E G B D A
G69 - G B D E A
A11 - A D E G B
Bm b6 11 (no5) (this is where it gets a bit risky, use it wisely) - B D G A E
Cmaj13 - C E G B D A
D69sus4 or Dsus24 add6, or any other name that describes all the notes - D G A E B
