What laws said that citizens could not be denied the right to vote based on their race ?

The correct answer is a change in society and its values

After returning home from World War II, veteran Medgar Evers decided to vote in a Mississippi election. But when he and some other black ex-servicemen attempted to vote, a white mob stopped them. "All we wanted to be was ordinary citizens," Evers later related. "We fought during the war for America, Mississippi included. Now, after the Germans and Japanese hadn't killed us, it looked as though the white Mississippians would. . . ."

The most basic right of a citizen in a democracy is the right to vote. Without this right, people can be easily ignored and even abused by their government. This, in fact, is what happened to African American citizens living in the South following Civil War Reconstruction. Despite the 14th and 15th amendments guaranteeing the civil rights of black Americans, their right to vote was systematically taken away by white supremacist state governments.