The final numbers in the sequence are …5, 7, 11, 9, 8, 6.

They reflect the number of letters in each sign of the Zodiac, beginning with the first:

5 = ARIES
6 = TAURUS
6 = GEMINI
6 = CANCER
3 = LEO
5 = VIRGO
then…
5 = LIBRA
7 = SCORPIO
11 = SAGITTARIUS
9 = CAPRICORN
8 = AQUARIUS
6 = PISCES

I was intrigued by the cleverness of several other answers, notably the one that noted that the numbers also matched up with the number of letters in the names of the Seven Dwarfs. The only thing preventing me from counting that answer as correct is the fact that there’s no order to that sequence… not alphabetically, by introduction, etc. Darned clever, though!