Let x be a real number such that \sin ^{10} x+\cos ^{10} x=\frac{11}{36}. Then \sin ^{12} x+\cos ^{12} x=\frac{m}{n} where m and n are relatively prime positive integers. Find m+n.
Let x be a real number such that \sin ^{10} x+\cos ^{10} x=\frac{11}{36}. Then \sin ^{12} x+\cos ^{12} x=\frac{m}{n} where m and n are relatively prime positive integers. Find m+n.