The day I said goodbye to Cuba
28 May 2014 Last updated at 03:00 BST
In 1980, more than 10,000 Cubans packed into the Peruvian embassy grounds in the capital Havana and asked for asylum.
This event led the Cuban President Fidel Castro to announce that anyone who wanted to leave Cuba could do so.
The ensuing mass exodus to the US is known as the Mariel Boatlift.
Mirta Oijto was one of many that made the journey for a new life.
Witness is a World Service radio programme of the stories of our times told by the people who were there.
Produced by Simon Watts and Directed by Claire Tailyour