As above, ebay and amazon have many variations of relay timer modules. Put the word 'cycle' somewhere in the search field.
If you really want to build a circuit from scratch, then one 555 astable circuit can do what you want - on paper. The total cycle period is 11-15 minutes, a looooong time in R-C timer land. Multi-minute R-C timers are not very stable, and their performance changes with temperature and aging.
I recommend a counter-based circuit rather than one or two 555's. Look into the CD4060 oscillator/divider. My first thought goes like this:
1 - CD4060
2 resistors (oscillator)
1 capacitor (oscillator)
1 capacitor (decoupling)
2 - 1N914 or 4148 diode (decoding)
1 - 2N7000 (relay driver)
1 - 1N914 (relay coil suppression)
The total body count is less than that of two 555 monostables in a series loop, and almost equal to a single 555 astable circuit.
ak