Let the area of the region \( \{(x, y) : x - 2y + 4 \ge 0, \, x + 2y^{2} \ge 0, \, x + 4y^{2} \le 8, \, y \ge 0\} \) be \( \dfrac{m}{n} \), where \( m \) and \( n \) are coprime numbers. Then \( m + n \) is equal to ______________.
