6 & 11? Well, mostly.
To start with, since a year is one day longer than a simple 52 weeks (365 = 52*7 +1), calendars would rotate on a 7-year basis. But we've got these leap-years in there, which mix things up a bit.
But there are still only 14 calendars available under the current system: seven calendars with Jan 1 falling on Sun, Mon, ... Sat, in a non-leap year, and another seven with Jan 1 on Sun, Mon, ... in a leap year.
Normally, the same day of the year will fall one day earlier the next year (e.g. if your birthday is a Friday one year, it should normally be a Saturday the next year). If there's a leap year, it'll skip a day to the Sunday (366 = 52*7 +2). This leads to a six-year cycle for a bunch of years (there often being only a single leap year within a six-year (or seven-year) interval).
The apparent 11-year interval is a bit more complicated, but the underlying issues are the same. (And I'm too tired to actually go through it just right now.)
[Edited to correct the number of days in a year. Oops.]