In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at \(50\) miles per hour along the highways and at \(14\) miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area of this region is \(\frac{m}{n}\) square miles, where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n\).

(第十八届AIME1 2000 第13题)