I think that King's background as a Christian minister helped him greatly.
First, the clergy held an important place in the black community at the time. As a member of the clergy, King had credibility with other African Americans. Second, because of the religious focus of so much of King's rhetoric, he was able to seem more acceptable to many white Americans. He was using a vocabulary and a set of references that was well-known to and well respected by white Christians. This made it much easier for them to respect and accept him than it would have been had he been a secular person or (for example) a Muslim like Malcolm X.
Books can be written about this particular topic. I think there are many books already out there about this topic. Dr. King possessed so many personal qualities that made him an effective Civil Rights leader. I think that his own middle class and stable background helped to contribute to a grounding that allowed he and his narrative to be effectively embraced by both Black and White Americans. While he was not in control of this narrative, it did benefit him. For example, he was able to speak of the first time he was called a racial epithet as a child, by a White child and having to tell his parents, with them explaining the implications to him. The fact that King grew up in an area where children of both races could coexist was something that he was able to use in bringing people together. This appealed to both social orders and increased his effectiveness. Another quality that he possessed was similar in his being able to bring the realm of social and spiritual change into one harmonious convergence. King understood that the political ends of the Civil Rights Movement would only gain traction if its morality could be fully evoked. When Dr. King spoke of Civil Rights, he was able to make it a moral issue, making it more receptive to people who might have possessed political fear about its tenets. This allowed him to become more effective in being able to communicate its message to all Americans. Finally, I do not think that America has seen a better orator and speechwriter than Dr. King. The templates offered in his speeches have served to inspire so many that have followed him. Simply put, Dr. King could deliver a speech. This increased his appeal because so many began to identify him with the movement, something that for the most part worked because he was able to articulate its vision with so much clarity and precision. The ideas of "the dream," the "mountaintop" "the promissory note," and "the fierce urgency of now" are but a few of the metaphors that Dr. King was able to adopt regarding the need for social, economic, and political change. Such vivid imagery allowed King to be very effective in seeking to transform what is into what should be.
I believe Dr. King was super courageous. He was also full of integrity. He had the stemina to make ideals become realities. He was forgiving and caring. He was rock solid and amazing.