\[\large \displaystyle \sum_{n=1}^{10} {i^{\frac{1}{n}}} = a + bi\]

In the equation above, \(a\) and \(b\) are positive real numbers. Find the value of \(\left\lfloor a \right\rfloor - \left\lceil b \right\rceil\).

**Notations:**

- \(i = \sqrt{-1}\) denotes the imaginary unit.
- \(\lfloor \cdot \rfloor\) denotes the floor function.
- \(\lceil \cdot \rceil\) denotes the ceiling function.

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