Lenovo X121e 3G with ModemManager

Recently, I tried to get 3G working on my Lenovo ThinkPad X121e - it has an Ericsson F5521gw mobile broadband card. This is supported by ModemManager, but all I got were unknown errors (276 and 272). Searching online, there were very few results (hence this short note) - just previous unrelated Linux kernel issues. I found someone with the same problem on Fedora, but no solution, so I started off by filing a bug report with Debian....