The game Flipper is played with 2 coins which may have any integer denomination from 1 to 99, inclusive. The coins are tossed, and the value of the toss is the sum of the denominations of those coins that show heads. The higher sum wins. In case of a tie, the game is replayed.

Two people play this game. One person has coins valued 1 and X, the other person has 5 and X. It is found that the game is fair, that is, the two people win in exact proportion to the total value of their coins.
What is the value of X?