For \( t > -1 \), let \( \alpha_t \) and \( \beta_t \) be the roots of the equation \( \big((t+2)^{1/7}-1\big)x^2+\big((t+2)^{1/6}-1\big)x+\big((t+2)^{1/21}-1\big)=0 \). If \(\displaystyle \lim_{t\to -1^+}\alpha_t=a \) and \(\displaystyle \lim_{t\to -1^+}\beta_t=b \), then \( 72\,(a+b)^2 \) is equal to ______.
