\(\Delta\)**ABC** is an equilateral triangle with side length 1. **AC, CB** & **AB** are extended respectively to **D, F** & **E** such that **E** is a point on segment **DF**.

Given that, lengths: \[\text{CD} =10 \quad,\quad \text{BF}=1.\]

If the length of segment \(\color {Blue} {\text{BE}} \) can be expressed as \(\frac ab\) where \(a\) & \(b\) are coprime positive integers, then find \(a+b\).

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