We use, "I can't complain." in the US, too. But never, "mustn't grumble".

Only in Britain! This is a very typical British response, which explains a lot about the British psyche. Here are some articles about it: http://www.lastwordonnothing.com/2014/01/24/mustnt-grumble/ http://www.telegraph.co.uk/culture/11146551/Trust-an-Englishman-to-have-the-last-word.html

I agree with "Business English Ed," "Can't complain" is common in the U.S., and I agree with Giulia Monaco that is something older people say. I THINK the meaning is "because I am old, I am always experiencing minor aches and pains, but they aren't bad, and given my age I can't complain." In Gilbert and Sullivan's "Princess Ida," a character sings a comic song about his frustration because he WANTS to grumble, and the people around him thwart him by giving him everything he wants: "Ah! Oh, don't the days seem lank and long When all goes right and nothing goes wrong, And isn't your life extremely flat With nothing whatever to grumble at!" http://diamond.boisestate.edu/gas/princess_ida/webop/pi_23.html

I would use 'can't complain' if I am feeling okay and nothing is particularly wrong. I have never heard anyone use mustn't grumble as a response though. Hope this helps

You sure can, especially in British English. Just bear in mind that 'mustn't grumble' in particular has a humorous to it.