doubleBooked.js

var
    toAdd = true,
    notToAdd = false,
    events = [
        {start: 1, end: 5},
        {start: 2, end: 3},
        {start: 4, end: 6},
        {start: 7, end: 8},
        {start: 9, end: 10},
        {start: 10, end: 11},
        {start: 11, end: 11}
    ];

function step(head, isAdd, events, intersect) {
    var
        neck = events.shift(),
        tail = events;

    if (neck === undefined) {
        return isAdd
            ? intersect.push(head) && intersect
            : intersect;
    } else {
        var
            headEnd = head.end,
            neckEnd = neck.end;

        return neck.start > headEnd
            ? isAdd
                ? step(neck, notToAdd, tail, intersect.push(head) && intersect)
                : step(neck, notToAdd, tail, intersect)
            : headEnd > neckEnd
                ? step(head, toAdd, tail, intersect.push(neck) && intersect)
                : step(neck, toAdd, tail, intersect.push(head) && intersect);
    }
}

function doubleBooked(events) {
    var
        sortedEvents = events.sort(function (a, b) {return a.start - b.start; });

    return step(
        sortedEvents.shift(),
        notToAdd,
        sortedEvents,
        []
    );
}

console.dir(doubleBooked(events));