Not entirely true Alec. But shortly after they elected record numbers of Black representatives in the late 1800's, which are still records, many states passed laws, (literacy, etc.), which effectively eliminated any real opportunity for them to vote until the 1964/1965 changes under Johnson.
One of the more interesting things reading that stretch, Kennedy probably could not have had the changes made because he did not have near the political clout and favors owed him that Johnson did.
"First, they had to win the civil war. After that, the 15th amendment was passed guaranteeing the right to vote to persons regardless of race.
As a matter of fact, right after the civil war, blacks were able to vote in such large numbers that they elected what is still a record of black representatives at the federal, state and local levels."