In a large bowl, combine orange juice, lime juice, and salt.
Cut melons into quarters, discard seeds, and cut off and discard peel. Cut fruit into 1-inch chunks; add to orange juice mixture. Cut mint leaves lengthwise into slivers. Add to bowl and mix gently to coat. Cover airtight and chill at least 1 hour or up to 4 hours.
Just before serving, mix marinated melons gently and sprinkle with feta cheese.