To make a simple syrup, combine sugar, salt, and ½ cup water in a small pot. Bring to a boil. Stir, and reduce heat to medium high. Stir occasionally until sugar is dissolved, approximately 5 minutes.
Add the lemon balm to the syrup. Push the leaves down with a spoon to submerge them in the syrup. Let the simple syrup cool.
After 10 minutes, remove the lemon balm leaves from the simple syrup.
Add 6 cups of water, lime juice, lemon juice, and all of the simple syrup (~1/2 cup) to a pitcher. Stir well, and chill.