We actually export a huge amount of rice. https://fas.usda.gov/data/commodities/rice
(3 million tons exported, to Cuba's 200k total production). We're actually the fifth largest exporter.
We also produce more sugar cane, but Brazil is the real power player there.
Cuba wouldn't be alone in being injured by US agricultural exports. Our volume and low cost can, for example, make people prefer imported American grains over domestic production, even if they're different types.