MathNet 2011 Question 11

Suppose $f(x) = |\lg(x+1)|$ and real numbers $a, b$ ($a \lt b$) satisfy $f(a) = f\left(-\frac{b+1}{b+2}\right)$, $f(10a + 6b + 21) = 4\lg 2$. Find the values of $a, b$.