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Technically 11th chords include a root, 3rd, 5th, 7th, 9th and 11th. But '11' is also used to mean a 7th chord with an added 11th and no 9th (sometimes called 7add11) In addition, C11 is sometimes used as an (incorrect) shorthand for C9sus (R, 4, 5, ♭7, 9, ♭11) which has no 3rd. So the 'rare' 3rds ar bracketed below. The only common 'real' 11 chord is a min11 chord. #11 chords, however are often found.
The most common the above are Cm11, Csus11, Cmaj7(#11) and C7(#11) The latter two are often p layed without 5ths
7-note (13th chords) 13th chords technically contain root, 3rd, 5th, 7th, 9th, 11th and 13th (all 7 notes). However the 11th, unless on a min13 chord is very rarely intended, the 9th often (but not always) is, and unless indicated otherwise, as a natural 9th (D on a C13). Often a 13th chord just implies root, 3rd, 5th, 7th and 13th (ie C7add13) unless other degrees are stated (eg. C7(b9/13). Some but not all 13th chords are listed below, although you should be able to derive most from those below.