validation booking room outside range?

#Code validation Booking

  $request->validate([
        "start_date" => [
            "required",  
            function ($attribute, $value, $fail) use ($request) {
                $booking = BookingTransaction::where('meeting_room_id', '=', $request->meeting_room_id)->where([
                    ["start_date", "<=", $request->input('start_date') . ' ' . $request->input('start_time')],
                    ["end_date", ">=", $request->input('start_date') . ' ' . $request->input('start_time')],
                ])
                ->orWhere([
                    ["meeting_room_id",'=',$request->meeting_room_id],
                    ["start_date", "<=", $request->input('start_date') . ' ' . $request->input('end_time')],
                    ["end_date", ">=", $request->input('start_date') . ' ' . $request->input('end_time')],
                ])
                ->first();
                if ($booking) {
                    $fail(
                        sprintf("Room meeting has already been booked. Please, try booking again outside this range.",
                            CarbonCarbon::create($booking->start_date)->format("d M Y H:i"),
                            CarbonCarbon::create($booking->end_date)->format("d M Y H:i")
                        )
                    );
                }
            },
        ],
    ]);

#problem

The code above explains the validation if the user adds a booking schedule in the time range between start_date : 2022-10-10 11:00:00 to end_date:
2022-10-10 15:00:00, it will fail,
now I want to validate if the user makes a booking outside the range between start_date:
2022-10-10 11:00:00
until
end_date:
2022-10-10 15:00:00, it will fail,
for example:
if the user makes a booking between:
start_date: 2022-10-10 09:00:00 to end_date: 2022-10-10 16:00:00 will fail ,
how to do above validation ?