The Planck mass is defined as $m_p = \sqrt{\frac{\hbar c}{G}}$, where $\hbar \approx 1.05457 \times 10^{-34} \text{ J}\cdot\text{s}$, $c \approx 2.99792 \times 10^8 \text{ m/s}$, and $G \approx 6.67430 \times 10^{-11} \text{ m}^3\text{kg}^{-1}\text{s}^{-2}$. What is the value of the Planck mass in micrograms ($\mu\text{g}$)?