What is the converted mana cost of a spell with {X} when cast with the Miracle mechanic?
The CMC is 9.
The XX in the mana cost and the X in the alternative cost are related. In your example, you chose X = 3, so the Converted Mana Cost (CMC) becomes 3+3+3 = 9. You only pay 3WW, but spells asking for the CMC of a spell, permanent, or card don't care about what you actually pay/have paid, they only care about what's printed in the upper right corner (usually) of a card.

How to calculate the CMC:

202.1. A card’s mana cost is indicated by mana symbols near the top of the card. (See rule 107.4.) On most cards, these symbols are printed in the upper right corner. Some cards from the Future Sight set have alternate frames in which the mana symbols appear to the left of the illustration.
202.3. The converted mana cost of an object is a number equal to the total amount of mana in its mana cost, regardless of color.
202.3b When calculating the converted mana cost of an object with {X} in its mana cost, X is treated as 0 while the object is not on the stack, and X is treated as the number chosen for it while the object is on the stack.

Spells don't care about alternative costs:

117.9c. An alternative cost doesn't change a spell's mana cost, only what its controller has to pay to cast it. Spells and abilities that ask for that spell's mana cost still see the original value.

The X in the alternative costs is the same X as those in the mana costs:

107.3g All instances of X on an object have the same value at any given time.