Place jicama in a bowl, sprinkle with salt and sugar, and add the juice of 1 lime. Let jicama stand 15 minutes. While jicama softens, work on the rest of your meal.
Arrange romaine on a serving plate. Top romaine with jicama. Juice 1 lime into a small bowl, add cilantro and cumin. Whisk in extra-virgin olive oil in a slow stream. Pour dressing over salad and season with salt and pepper.