Chantelle had two candles, one of which was \(32\) cm longer than the other. She lit the longer one at \(3\) p.m. and lit the shorter one at \(7\) p.m. At \(9\) p.m., they were both the same length. The longer one was completely burned out at \(10\) p.m. and the shorter one was completely burned at midnight. The two candles burned at different, but constant, rates. What was the sum of the original lengths of the two candles?
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