Hi.
I don't know a lot about hi-fi, except what my ears are telling me.
I received a Cambridge Azur's 540 amp. I coupled it with my Rogers LS3/5a speakers.
Rogers' are 11 ohms impedance speakers. In Azur's doc, they suggest speakers to be in the 4 to 8 ohms range.
The obvious effect (to my ears) is low volume. Are there other acoustic effects to the pairing of those two?

That is all fine. Neither the amp nor the speakers will suffer. Mismatch may only become dangerous if the speakers' impedance is lower than the minimum rating of the amp.
The efficiency of the old KEF Bextrene diaphragms is quite low, therefore the low volume. But they sound very good!

Edit: of course the high impedance additionally results in lower output volume, as you already noted

See this thread for all you ever cared to know about speaker impedance:
Help on IMPEDANCE