They belong to every key Felix. Or, to put it another way, EVERY major key has seven 7th chords and seven 6th chords - (one for each note of the scale)
And every minor key has even more than seven.
Here are the 6th & 7th chords that belong to C major:
C6 - C major7
D min6 - D min7
E min (b6) - E minor 7
F6 - F major7
G6 - G7
A min (b6) - A min7
B dim add b6 - Bm7b5
*Some of those chord names aren't seen in real music. For example, Bdim add b6 has exactly the same notes as G7. (BDFG & GBDF).
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