Martin Luther King Jr.'s attempts to gain equality met with slow, qualified success over time. Coming on the scene in earnest in 1955 during the Montgomery Bus Boycott, you can say that his effort to desegregate the busing system there were entirely successful, but it took nearly a year and another Supreme Court ruling in his favor for it to happen. Both that decision and the Brown vs, Board of Education decision a year earlier were not a result of any of MLK's efforts, and had a huge impact on his degree of success.
His March on Washington in 1963 was important, and historically significant, but did little to persuade our government to act any differently or more quickly for civil rights.
His "Letter From a Birmingham Jail" is considered one of his more important pieces of writing, but at the time it had little impact at all.
So I would say MLK's successes were on an individual basis, place by place, case by case, and had a limited effect on the big picture of equality at the time. We celebrate and recognize them more today because of their significance historically, while at the time, the FBI is still investigating for being a supposed communist. It was only in combination with others, and the government in specific cases, that civil rights was successful.