You go from -more or less- 11 days to 11.000 days. At -say for easy numbers- 333 days a year, you get to 11.000 / 333, which is about 100/3 which is about 30, 30 days...
Back of a napkin calculations greatly help in getting a better sense of these numbers.
I agree with your thinking and method and think that is a good way to get to these difference.
However, sitting down and running the numbers quickly isn't intuitive to the average person, and neither is quick estimates like that.
11 days vs 31.5 years is a fast and effective way to break it down to the average person though.