President Kennedy didn't negotiate with the Soviets. He instituted a naval blockade of Cuba and informed the Russians we would attack Cuba unless the missiles were removed. It was an ultimatum and the Soviets, wanting to protect their investment in Castro's regime backed down. It wasn't due to sweet talking with them that the world came down from the brink of a nuclear war.
"Show me just what Mohammed brought that was new, and there you will find things only evil and inhuman, such as his command to spread by the sword the faith he preached." - Manuel II Palelologus