Lone ant on a cube

There exists a cube in space. One of its corners is marked. An ant starts from a random unmarked corner and moves only along the edges of the cube. If the ant is at a corner, it chooses an edge randomly and moves to an adjacent corner with uniform velocity.The ant starts moving when the clock is at zero, and moves continuously with constant speed. If it is known that the ant traverses a side of the cube in one second, find the expected time elapsed(in seconds) before it reaches the marked corner for the first time. If the answer can be expressed as \(\frac{a}{b}\) in simplest form, enter \(\frac{(a+5)}{b}\).

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