How is the theme of Langston Hughes's poem "A Dream Deferred" reflected in Martin Luther King's I Have a Dream speech?

The theme Langston Hughes's poem "Dream Deferred" shares in common with Martin Luther King Jr.'s I Have a Dream speech is the idea that, although racism shrivels and cripples humanity, it also, eventually, leads to enough anger to empower mankind to rise against it.

Hughes's poem begins with a lot of imagery that captures waste and destruction. For example, the image of a shriveled raisin in the sun can further be understood as an image of a grape that has been scorched by the sun, leaving it devoid of its potential as a grape. Plus, the image of "rotten meat" can further be understood as the image of not just the meat of a dead animal but of meat that has gone uneaten so long that it is now rotten, no longer nutritious, and even deadly to anyone who tries to eat it.

Yet, Hughes ends his poem with a very powerful rhetorical question:

Or does it explode?

By asking if a deferred dream explodes, Hughes is asking if unfulfilled dreams do not die, but rather become so powerful that the dreamer eventually bursts in a release of energy so strong that the dreamer is finally stirred to take actions to fulfill his or her dream. Hughes's rhetorical question captures images of African Americans "exploding" to fulfill their dreams by fighting for their liberties during the Civil Rights Movement.

In his speech, Martin Luther King, Jr. similarly describes racism and oppression as destructive forces by likening them to the image of the sun and what the sun can scorch to death, just as Hughes speaks of the sun shriveling a grape into a raisin:

This sweltering summer of the Negro's legitimate discontent will not pass until there is an autumn of freedom and equality.

In using the image of a "sweltering summer," King is speaking of oppressive heat, the kind of heat that turns everything brown in the summer so that it dies and falls in the autumn, leaving room for new birth and rejuvenation.

Also, just as Hughes ends with the powerful rhetorical question asking if unfulfilled dreams "explode," King similarly speaks of African Americans finally "exploding" to fulfill their dreams. One of the most obvious places in which he speaks of African Americans becoming empowered enough to fight against oppression is in the following:

The whirlwinds of revolt will continue to shake the foundations of our nation until the bright day of justice emerges.

In addition, each time King begins a statement towards the end of the speech with "I have a dream," he is speaking of African Americans becoming empowered as a result of being angered by oppression, eventually leading them to "explode," or rise up and fight for justice.