Counting/Digital clock/Carnival steps/Exercise

We consider a digital clock, which exhibits ${}24$ hours, ${}60$ minutes and ${}60$ seconds. However, during carnival, it does not run in steps of seconds, but it adds, starting from the zero position, in every step ${}11$ hours, ${}11$ minutes and ${}11$ seconds. Does, with this way of counting, every possible digital display appear? After how many steps does the zero position reoccur for the first time?

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