It's not an extra second, a clock might go 23:59:59 - 00:00:00 - 00:00:01 or 23:59:59 - 24:00:00 - 00:00:01. Both are equivalent and have the same meaning, with

It's not an extra second, a clock might go 23:59:59 - 00:00:00 - 00:00:01 or 23:59:59 - 24:00:00 - 00:00:01. Both are equivalent and have the same meaning, with the only difference that 00:00:00 belongs to the new day and 24:00:00 belongs to the old day (despite both being the exact same moment in time). Of course clocks choose the former for simplicity, but for stating the end of an interval 24:00 can be clearer and preferred. 24:00 has no duration, it's only an instant in time. The same could be said about 11:34 of course, as long as you assume 11:34 to mean 11:34:00.0000000000000000000000 and not the interval from 11:34 to just before 11:35.