Confusing sines and cosines

Level pending

The value of \[ \cos^{2} 55^{\circ} +\cos 55^{\circ} \cos 35^{\circ} \sin 10^{\circ} + \sin 20^{\circ} \cos^{2} 5^{\circ} \] can be expressed as a fraction \( \frac{a}{b} \), while \( a \) and \( b \) are positive integers which are relatively prime. Find \( a+b \).

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