You should quickly find sources converge on a coefficient to convert dose into cancers. Modern science has quantified this rather well.
LNT estimates that the risk of premature death from radiation-induced cancer is around 5% per sievert or 0.5% per 100 mSv of exposure.
The units are easy to mess up, so I'll rewrite the above coefficient:
0.00005 cancers / mSv
There are more variables you could put into this. I mean, our linear (as in the LNT model) assumption is, in effect a model. You could replace that model with a sophisticated computer code that takes in all kinds of adjustments, but I'm not interested in that accuracy here. One very notable correction is fractionated versus non-fractionated dose. Nuclear industry workers who get a large dose through a single work operation get something like twice the corresponding cancer risk, as opposed to getting that same dose distributed over a longer period of time. For Mars colonization, I would imagine the dose is pretty constant. But anyway, moving on:
(0.00005 cancers / mSv) x (11 mSv per year) = 0.00055 cancers / year
I don't know how long you'd expect to live on Mars. Let's say 40 years.
(0.00055 cancers / year) x (40 years) = 0.022 cancers --> 2.2% chance of getting cancer
Had this number been much closer to 1.0, then different statistical equations would be needed. For reference, these days the "normal" chance of someone getting cancer and dying from it is something like 23%.
This answers half your question, and I'm going to leave it here. I don't know if I believe that a year on Mars will result in 11 mSv. With some very cursory looking online about the subject, I'm starting to get a picture that it depends almost entirely on assumptions about how the colonists spend their time. Assume that they're under a rock all day, and the dose could drop to near zero. This isn't physically impossible. Just put them under 10 tons/m^2 of dirt. Finished. Radiation requirement met. On Earth this would be workable, even if unpleasant. Design of the facilities on Mars would be subject to... more constraints.