What relationship did the African American struggle for for civil rights have with other American minorities and how did these minorities benefit?
In the modern Civil Rights movement of the 1950s and 60s, tactics of Civil Disobedience, economic boycott, public peaceful protest and consistent non-violence were used that, over time, enjoyed success at getting basic equality for African-Americans. The move for Latino rights, especially for farmworkers on the West Coast, grew around Cesar Chavez and the United Farm Workers, who copied many of those same techniques and used them well throughout the 1980s even, to obtain better pay, worker safety rules and injury compensation. While the two movements did little to directly help each other, they did use many of the same methods.
The African American civil rights movement did not really coordinate with any other ethnic group's rights movement. I do not really see them having a relationship with one another.
However, the black rights movement surely helped rights movements such as the one for the rights of Hispanics. Because blacks had successfully fought for their rights, Hispanics were inspired to fight for theirs. Because blacks had won rights, it was easier for whites to accept the idea of rights for other minorities.
The black rights movement also showed other minorities (and women and gays, among others) what tactics worked in a rights movement.
The group that benefited the most from the Civil Rights movement was the woman's movement. When the Civil Rights issues were exploding across our nation the woman's rights movement was stating to build momentum.
As African American women stepped out to advocate for themselves, Caucasian women also stepped forward. Tired of the increasing divorce rate, being treated as second class citizens in the work place, low pay for positions that men made much more money for performing, the women began to take bigger steps on their own.