Having the right to vote and being able to exercise that right are horses of a different color (no pun).
http://www.history.com/topics/black-history/voting-rights-act
"...After the U.S. Civil War (1861-65), the 15th Amendment, ratified in 1870, prohibited states from denying a male citizen the right to vote based on “race, color or previous condition of servitude.” Nevertheless, in the ensuing decades, various discriminatory practices were used to prevent African Americans, particularly those in the South, from exercising their right to vote.
During the civil rights movement of the 1950s and 1960s, voting rights activists in the South were subjected to various forms of mistreatment and violence. One event that outraged many Americans occurred on March 7, 1965, when peaceful participants in a voting rights march from Selma, Alabama, to the state capital in Montgomery were met by Alabama state troopers who attacked them with nightsticks, tear gas and whips after they refused to turn back. Some protesters were severely beaten, and others ran for their lives. The incident was captured on national television.
In the wake of the brutal incident, Johnson called for comprehensive voting rights legislation. In a speech to a joint session of Congress on March 15, 1965, the president outlined the devious ways in which election officials denied African-American citizens the vote. Blacks attempting to vote often were told by election officials that they had gotten the date, time or polling place wrong, that they possessed insufficient literacy skills or that they had filled out an application incorrectly. Blacks, whose population suffered a high rate of illiteracy due to centuries of oppression and poverty, often would be forced to take literacy tests, which they inevitably failed. Johnson also told Congress that voting officials, primarily in Southern states, had been known to force black voters to “recite the entire Constitution or explain the most complex provisions of state laws,” a task most white voters would have been hard-pressed to accomplish. In some cases, even blacks with college degrees were turned away from the polls..."