This year’s Cannes Film Festival saw its fair share of high-profile projects, but no premiere is sparking as much Oscar buzz as Loving, Jeff Nichols’ look at the young interracial couple who were arrested in 1958 simply for marrying each other.

Australian actor Joel Edgerton and Irish-Ethiopian actress Ruth Negga star as Richard and Mildred Loving, who were convicted and exiled from their home state of Virginia shortly after their marriage. The pair eventually took their case to the Supreme Court, which subsequently declared bans on interracial marriage unconstitutional, but while the couple have left a lasting impact on the fight for American civil rights, Richard and Mildred were both fairly private people — and their story has gone largely untold until now.

Sitting down with PEOPLE and EW at Cannes, Edgerton and Negga spoke about why they were both so eager to tell the story of this quiet but powerful pair.

“Dramatically, I was drawn to this struggle, this very silent struggle of two people who were just so put upon that they didn’t really have a voice or the actions to navigate or overcome this situation,” Edgerton says. “So there was this sort of very gentle but monumental civil rights shift in America that not enough people know about.”

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Nichols, who most recently worked with Edgerton on the sci-fi thriller Midnight Special, has spoken about how he became fascinated by Richard and Mildred’s story after seeing the 2011 HBO documentary The Loving Story.

“I’d seen the documentary, and I was so struck by this couple,” Negga says. “Individually, but also their love for each other just seemed such a beautiful, delicate, rare thing. I felt such outrage on their behalf, like many others, that the simple act of wanting to be married to another human being would incur the wrath of the law and also make people really angry. So angry — violently angry. I was just so shocked by that.”

Focus Features will release Loving in limited release on Nov. 4. Watch the exclusive video above for more from Edgerton and Negga.

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