I own a digital 24-hour clock (i.e., a military time clock) that displays in HH:MM format. Each digit uses the standard seven-segment display in which seven lights toggle on or off to form numbers, as ...

At 6 A.M. or P.M. (it doesn’t matter which), a clock’s minute hand and hour hand point in opposite directions, forming a straight line across the clockface. When is the next time this will happen?