1. Given the equation: $$3f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 10$$

2. Replace $$x$$ with $$\frac{1}{x}$$ in the original equation:
   $$3f\left(\frac{1}{x}\right) + 2f(x) = x - 10$$

3. Now, we have two equations:

$$3f(x) + 2f\left(\frac{1}{x}\right) = \frac{1}{x} - 10$$

$$3f\left(\frac{1}{x}\right) + 2f(x) = x - 10$$

1. By adding the two equations, we can find $$f(x)$$:

$$5f(x) = \frac{3}{x} - 2x - 10$$

1. Now, let's differentiate both sides with respect to $$x$$:

$$5f'(x) = -\frac{3}{x^2} - 2$$

1. Now, we can find the values for $$f(3)$$ and $$f'\left(\frac{1}{4}\right)$$:

$$f(3) = \frac{1}{5}(1 - 6 - 10) = -3$$

$$f'\left(\frac{1}{4}\right) = \frac{1}{5}(-48 - 2) = -10$$

1. Finally, calculate the expression we are interested in :

$$\left|f(3) + f'\left(\frac{1}{4}\right)\right| = \left|-3 - 10\right| = 13$$