I would use Symbolic Math Toolbox to solve the problem analytically:
x = [74 29 21 12 8 5.7 4.4 3.6 2.1 1.8 1.5 1.0 0.7];
y = [80 131 189 270 320 407 450 530 620 686 740 900 1095];
s = spline(x, y) % create pp object
xq = min(x):max(x);
s1 = spline(x,y,xq); % just for plot
plot(xq,s1)
hold on;
yline(600); % serch solution roughly
ax = gca;
ax.XTick = s.breaks;
xline(s.breaks,':');
hold off;
xlim([0.82 7.35])
ylim([478 718])
The solution seems to lie in the 5th section.
The coefficients of the function corresponding to the 5th sections are
s.breaks
s.coefs(5,:)
Extract coefficients
x1 = s.breaks(5)
x2 = s.breaks(6)
a = s.coefs(5,1)
b = s.coefs(5,2)
c = s.coefs(5,3)
d = s.coefs(5,4)
Use Symbolic math to analytically solve the problem
syms x
f(x) = a*(x-x1)^3+b*(x-x1)^2 + c*(x-x1) + d
sol = vpasolve(f==600,x,x1) % solutions at y = 600
x = 2.211 or something.
