Same five digits

Back in 2011, a magazine offered £15 for anyone who solved this puzzle first. It goes as follows:

I have written down three different 5-digit perfect squares, which between them use five different digits. Each of the five digits is used a different number of times, the five numbers of times being the same as the five digits of the perfect squares. No digit is used its own number of times. If you knew which digit I have used just once you could deduce my three squares with certainty.

What is the sum of my three perfect squares?

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