If \( 1 + \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}} + \frac{5-2\sqrt{6}}{18} + \frac{9\sqrt{3}-11\sqrt{2}}{36\sqrt{3}} + \frac{49-20\sqrt{6}}{180} + \ldots \) upto \( \infty = 2 + \left( \sqrt{\frac{b}{a}} + 1 \right) \log_{e}\!\left( \frac{a}{b} \right) \), where \( a \) and \( b \) are integers with \( \gcd(a,b)=1 \), then \( 11a + 18b \) is equal to \( \_\_\_\_\_\_\_\_ \).
