It is now between $10:00$ and $11:00$ o'clock, and six minutes from now, the minute hand of the watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now? Express your answer in the format of "HH:MM", where HH is the hour and MM is the minute, both as two-digit numbers. Calculate the sum of HH and MM.

Let's think step by step and output the final answer within \boxed{}.
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