Add mint leaves, lemon juice, and lime juice into a cocktail shaker. Muddle to break up the mint leaves with a cocktail muddler or flat end of a wooden spoon.
Add minced ginger, agave syrup, and light rum into the cocktail shaker along with ice. Give it a good shake.
Pour the mojito mixture into a tall glass (highball glass) with ice.
Top with club soda.
Notes
Taste after 1 ounce to see how you like it. You can always add more rum, but you can't take it away.