President John F. Kennedy and Soviet leader Nikita Khrushchev worked together independently of their military/security bureaucracies to resolve the issue. Both paid a price.  President Kennedy was murdered by the CIA and Joint Chiefs of Staff who were determined not to lose the Soviet enemy that justified their power and budgets.  Khrushchev was removed from power by Communist Party hardliners suspicious of accommodation to the capitalist enemy.  

After President Johnson destroyed himself in the military/security complex's Vietnam War, President Nixon renewed the tension reducing policy of President Kennedy.  The Strategic Arms Limitations Talks (SALT) and arms limitations agreements followed.  President Nixon topped them off by opening to China and replacing that tense relationship with the "one China" policy.  This was again too much for the US military/security complex, and they orchestrated with the Washington Post the "Watergate" scandal to remove him from office.